Beartrap Canyon, a Bureau of Land Management wilderness area east of Norris, is a steep gorge cut by the Madison River.
A hiking trail starts three miles down a dirt road from the Red Mountain Campground (about nine miles east of Norris on Highway 84) and runs seven miles up the canyon.
A dam at the southern end holds back Ennis Lake [1]; hiking is prohibited around the dam, forcing hikers to retrace their steps to leave the canyon. The trail is popular with both hikers and anglers and can get crowded on summer weekends.
Links:
[1] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/three-forks-and-the-madison-river-valley/e/ennis-lake